PHYSICA ELSEVIER Physica A 218 (1995) 1-18 Topology, dynamics and finite size effects of a kinetic growth model Ubiraci P.C. Neves, Roberto N. Onody Departamento de Ffsica e Informdtica, lnstituto de Ffsica de Sdo Carlos, Universidade de Sdo Paulo, Caixa Postal 369, 13560-970, Sdo Carlos, Salt Paulo, Brazil Received 10 March 1995 Abstract Ramified polymerization is studied through computational simulations on the square lattice of a kinetic growth model generalized to incorporate branching and impurities. The polymer configuration is identified with a bond tree in order to examine its topology. The fractal dimensions of clusters are obtained at criticality. Simulations also allow the study of time evolution of clusters as well as the determination of time autocorrelations and dynamical critical exponents. In regard to finite size effects, a fourth-order cumulant technique is employed to estimate the critical branching probability bc and the critical exponents ~, and ft. Finally, for the case when impurities are not present, the surface roughness is described in terms of the Hurst exponents. 1. Introduction During the last decades several models have been employed to investigate the poly- merization phenomenon. The simplest idealization of a polymer chain is the well-known random walk. If the polymer is not allowed to cut itself, then it is modelled by the self-avoiding random walk [ 1,2]. On the other hand, lattice animals, namely connected clusters of occupied lattice sites, provided a good model of branched polymers in dilute solvents in the high-temperature limit [ 3]. Many exact enumeration data are available [4-6]. The lattice animals without loops, i.e., trees, were also considered as good can- didates to describe polymers. Camacho et al. [7] worked out a systematic topological classification of trees with respect to the number of bonds and vertex type. An alternative way of studying the polymerization phenomenon is through the so- called kinetic growth model [ 8,9]. This is more realistic than the self-avoiding random walk in the sense that the growing end is repelled by the occupied sites. Recently, Lucena et al. [ 10] have generalized it to permit the branching of the polymer and Elsevier Science B.V. SSD10378-437 1 (95)00127- 1